Hi Nick, another user here.

Just in case you are not aware, I think you can achieve (most?) of what you are after if you use the CycleTravel website. (That works well on a smartphone, although a bigger screen is  an advantage; and obvs tap instead of click.)

There may be other/better tips from others, but this is how I would do it:

In My - Journeys, use Add to make a new folder eg named Favourites. In a stored journey, Insert Via Points to mark the start and end of a favourite section, and prune off the rest using the "Delete before / Delete after" functions that are accessed by clicking on the VP and then on the "More ..." button. Save the pruned routes into your Favourites folder. The whole set can be viewed on the map:  in My - Journeys, on the right of each folder is an icon like an unfolding map; click on that to display on the map all the routes in the folder, in different colours. Click on a route to open it for editing, extending it with added VPs to make a new route incorporating your favourite, saving that with a new name (I would save into a different folder to avoid mixing it with Favourites). 

Limitation: This method only directly seeds one favourite section into your new route, although obviously you can use VPs to include others. Opening another instance of Cycle Travel would let you see the whole set of Favourites at the same time as you edit your new journey.  

Thankyou so much Simon! I'm going to enjoy having a good play around that!